Modeling of 3D Fractal Images

Abstract

Fractals provide an innovative method for generating three-dimensional (3D) images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invarience and dimensionality. Images such as coastlines, terrains, cloud mountains,and most interestingly, random shapes composed of curves, sets of curves etc. present a multi-varied spectrum of fractals usage in domains ranging from multi-colored, multi-patterened fractal landscapes of natural geographic entities, image compression to even modeling of molecular ecosystems. Fractal geometry provides a basis for modeling the infinite detail found in nature. Fractals contain their scale-down, rotate and skew replicas embedded in them. Of the many different types of fractals that have come into limelight sins their origin, the fractals like the Koch curve, the Cantor set, the Fern leaf, the Sierpinski gasket have eluded both mathematicians and computer scientists alike. And the two-dimensional (2D), 3D versions of the same have been realised based on the starting axioms/generators. This paper explains the generation of 3D versions of the above fractals that gives a real-world look and feel in the world of fractal images.